Geometer's Sketchpad 17-gons

Geometer's Sketchpad - Circle Design

The Man Who Made Fractals Famous Dies at 85

Benoît Mandelbrot obituary
Mathematician whose fractal geometry helps us find patterns in the irregularities of the natural world

By the Numbers

Your students will enjoy these interesting numerical comparisons - data from 2000 and 2010.

http://www.newsweek.com/feature/2010/by-the-numbers-how-the-digital-revolution-changed-our-world.html?gt1=43002

And the Politicians Continue to Blame the Teachers

Benoit Mandelbrot Speaks at T.E.D.

The talk is hard to follow, especially for the lay person, but it it great to hear Mandelbrot speak.

Revisting Daniel Pink

I posted Dan Pink's T.E.D. talk about "What Motivates Us'' in a previous post. Here it is again with a great cartoon animation.

Primitive Cultures Develop Sesame Street

xkcd: One Two

Sent by my friend David. Thanks!

Quote of the Day - Grade Inflation

In American schools, grade inflation is so out of control that a B minus is a classroom teacher’s best and safest choice for indicating an actual grade of F.

Earl P. Bell
Letter to the Editor
New York Times
June 27, 2010

Quotes of the Day

Some freshmen do not know that “one-half and .5 represent the same number,” said Dennis Piontkowski, chairman of the mathematics department. “We don’t want to keep students in math classes forever, but you can’t just snap your fingers and bring them up to college level.”

and then too...

Students are leaving high school with a diploma, but “most are testing at middle-school reading comprehension” and many at elementary-school level, said James Sauvé, an English department instructor in charge of revising the remediation classes.

The remediation should be addressing 'how to be an effective learner' instead of explaining that .5 = 1/2. If a student had effective learning skills, he/she would have a command of basic skills before entering college.

And students should know that education takes work and failing is an option.

Thank you The Bay Citizen.

Grade Inflation

This is one of the ways grade inflation starts.

Face Memory Game

It was interesting to wander around the Washington.edu site and check out the different memory tests.

I will be using some of the games to help my students learn memorization strategies, specifically for addition and multiplication facts given that surprisingly many high school clients do not know these facts.

My elderly clients often have trouble remembering new facts, especially in regards to new technology. "Why on earth would you click on the Start Up button to turn your computer off?", was one of the comments I heard. There are physical changes that occur in the brain as humans age that make it more difficult for many people to learn new things, so it is not surprising that it takes some practice to learn how to program TIVO.

On the other hand, my teenage clients are able to remember all sorts of facts: phone numbers, how to use the many functions of their graphing calculators and cell phones, how to download and keep track of thousands of songs, and how to manage their social networking pages yet these same students cannot remember the product of 6 and 7. Even more disturbing is the fact that a number of the parents are likely to tell me that their children are incapable of memorizing their math facts rather than admit that their child might be a bit lazy or unmotivated to do the work.

Memorization takes work. And some memorization, such as math facts, may be tedious and unpleasant work. It has been my experience that most of the students lacking math facts are UNWILLING to do that work.

Crazy Things Can Happen When Math gets into the Hands of Legislators

I stumbled upon a blog post by divine caroline that stated that in Indiana

π = 4.

The blogger cited no references.

In my search to find the story, I found a treasure, The Straight Dope by Cecil Adams who may or may not, actually be Ed Zotti.


Cecil tells a great story about how an amateur, and possibly crazy, mathematician, Edward J. Goodwin, persuaded an Indiana Representative, in 1897, to introduce a House Bill #246 that would legislate:

π to be 4,

π = 3.2 in another instance, 

and π to be about 3.23 in yet a third instance. 

According to Adams, Bill #246 made it through the house.

Bill #246 also passed the Indiana Senate but before it could be enacted into law, a Purdue Professor, C. A. Waldo was able to point out the absurdity the idea to a Senator and Bill #246 was postponed, possibly infinitely, or until the end of time.

Ed Zotti as he appears on his Blog, The Barn House.

Apparently, the legislators didn't know their history as well as their math. Mathematicians had only been working on determining the value of π for roughly 3800 years by the time Goodwin appeared on the scene and decided not only to change the value of π, but its definition too.

Lesson #1 - Education has come a long way since 1897. Almost all of my students know that π is approximately equal to 3.14 and I want to believe it would take a lot of work to convince them otherwise.

Lesson #2 - It is still true today that it is sometimes dangerous to let mathematics and science get into the hands of legislators.

Lesson #3 - Passing and enacting a law have different meanings. Who would have ever thought it? So, even though Bill #246 was passed, in both houses, it was never a law on the books and to this day, people in all walks of life in Indiana are allowed to use π at the common value of 3.14, close enough for many purposes, the 14 digit accuracy of the TI-84, or the 2.7 trillion digit accuracy level determined by Monsieur Bellard of France, January of 2010, using his desktop computer. (Oh by the way, it took 131 days to complete and check the result, if you were thinking of choosing that option).

Do These Images Remind You of M.C. Escher?

These were created before Escher's body of work. They are by Ernst Haeckel. The recursive nature of the illustrations reminds one of fractals.

The drawings are fabulous! See more of them here.

Another Interesting Drawing Site

Check out this web-based drawing program. The options will be at the bottom of the screen.

Revisiting Daniel Tammet

Daniel Tammet is the man who memorized the digits of pi to over 22,000 places. This video tells about his life as a savant. An added bonus is that Kim Peek makes an appearance.

4-Day School Week

I have thought, for a long time, that a 4-day school week would be a great idea. Now, in Georgia, due to budget shortfalls, school districts are trying the idea. The students go to school for the same number of hours annually and they have longer school days. The great part is the 3-day weekend.

The kids love it. The teachers love it. Test scores have risen and attendance has improved. The parents, however, find it very inconvenient. The superintendent of one district makes a great point. She says that the school district is not in the business of providing child care. It has been a side benefit to providing education for the students and it is no longer in the position to provide such a service 5 days a week. It's a good point.

Going Deeper into a Fractal

 Check out this cool Fractal Video.

Paul Erdös Referred to Children as Epsilons*

Radio Lab is a fabulous radio show from WNZC. A program from October 2009 delves into numbers including the origin of Erdös numbers as well as some interesting stories of the idiosyncrasies of the prolific mathematician Paul Erdös, after whom the numbers were named. It is definitely worth a listen.

From Benford to Erdös



*The Man Who Loved Only Numbers, Paul Hoffman, Hyperion Press, 1998

The Amazing Power of Two!

This is a fun trick that kids can easily learn and wow their friends. It works because the chosen cards are in relative power of two positions guaranteeing that they will always land in the down position.

What math class? I dunno.

A recurring experience:

Question: "You are in the 10th grade? So, are you taking Geometry?"

Answer: "Yeah. I think. I don't know."

Question: "Could it be Algebra perhaps?"

Answer: "Yeah, I think that is it."


This actually happened, AGAIN, today when I was in town. It is mind boggling to imagine how a high school student is expected to do well in math when he/she doesn't even know what class they are enrolled in.

California: Algebra for all Eighth Graders

As often occurs, California policy makers have gotten it wrong.

Research has shown that students who successfully pass Algebra in middle school are more likely to enter higher education. Algebra has been labeled a "gate keeper" to higher education. Apparently, success in Algebra in the 8th grade, rather than later, is the number one indicator of whether a student will proceed to college. So, what is wrong the policy that requires all 8th grade students to take algebra? In quaint terms, this policy places the cart before the horse.

The reason a student is successful and passes algebra, no matter the age of the student, is that the he/she has a fluent understanding of some basic math concepts that support taking algebra. In other words, it isn't that the student takes algebra in the 8th grade... the success of the student depends on the fact that he/she is READY to take algebra in the eighth grade.

There are districts in California that have a "no fail" policy, also called "social promotion", in elementary school. In other words, whether or not a student understands essential curriculum, he/she is promoted to the next course until, voilà, the student arrives in an 8th grade algebra class without knowing:

How to do long division
How to do operations with fractions
Their multiplication facts
Their addition facts

Yet... the powers that be think that such a child is going to have more success in the future just for the reason that he/she is taking algebra in middle school when, in fact, it is the opposite. A child will be successful in algebra BECAUSE he/she has mastered a fundamental amount of mathematical thinking BEFORE taking an algebra class.

This Week in Mathematics Education

I was given a set of bulletin board framing strips to use in the classroom. They are made by a publisher, not a teacher. Check out the red polygon. Oh by the way, recall that 'oct' means 'eight'.


A student appears in a Geometry class (10th grade). The teacher soon finds out that he/she is performing a very low level (2nd grade is the estimate). He/she doesn't know the difference between a square and a rectangle, doesn't understand the concept of 'half', and doesn't know the answer to twelve divided by three, or three divided by one. The situation is not an isolated incident. The same teacher had a student this year, enrolled in Advance Algebra, who couldn't find page one of the math book, couldn't graph a point, and also didn't know his multiplication tables.

What if Social Promotion in the elementary grades is the official policy of the school district? At what point is a student retained? Apparently not in high school. An administrator at one of the high schools said that if a kid is in the 11th grade then he/she should be in Advanced Algebra because that is the age appropriate class, even though the student hadn't passed math for years. Apparently the previous classes are not called "pre-requisites" until college.

 Also in the news, U.S. Falls Short in Measure of Future Math Teachers. In my opinion, too many American elementary school and middle school teachers are under-qualified to teach math effectively. The comment at the end of the article by Dr. Gage Kingsbury, a senior research fellow at the Northwest Evaluation Association is ludicrous.

“...to suggest that you can’t be a good middle school math teacher unless you’ve taken calculus is a leap, because calculus isn’t taught in middle school. So I think they overreach a bit.”

It is essential that a teacher have a broad understanding of mathematics to be able to effectively teach Algebra and pre-Algebra, both of which are middle school courses.

Would we fire every doctor in the emergency room?

Dear President Obama,

"Every Central Falls teacher fired", was a headline in the news this week.

"The state’s tiniest, poorest city has become the center of a national battle over dramatic school reform. On the one side, federal and state education officials say they must take painful and dramatic steps to transform the nation’s lowest-performing schools."

But, as stated in my last post, the powers-that-be, in this case the Central Falls Board of Education, fail to recognize that the best predictor of low academic performance is poverty—not bad teachers.

Imagine an impoverished, inner city, hospital emergency room. Such an emergency room will see more violent crime trauma victims than an emergency room in a middle class suburb. Continuing with the metaphor... what if the the hospital board decided to fire all of the emergency staff at the inner city hospital because there were too many gunshot and stab-wound deaths as compared to the hospitals in the suburbs? Would anyone in their right mind consider this a good solution?

It is impossible to abstract student achievement from the social environment of the school and community. It is very difficult to inculcate students into an academic environment when the environment at home doesn't support that goal and that is the least of the problem. Teachers are dealing with students who may be carrying weapons, belong to gangs, come to school malnourished, are being abused, or live in homes where people are trading in narcotics or sex. We have students who have been shot, stabbed or raped, and who know more than one person who has been murdered, students who live in group homes, or worse, on the streets.

It is appalling that teachers should have to carry the brunt of these social problems. In similar circumstances we hail our police officers and firefighters as heroes. We praise hospital emergency room staff as courageous and saintly for the work they have chosen. Yet, teachers who are working to make positive differences in our at-risk youth, are metaphorically flogged and blamed for the educational outcomes of the people they are trying to help.

Teachers, who must often dedicate precious time nursing the psychic wounds of their students, may not be able to make measurable progress in "closing the achievement gap" or increasing standardized test scores, especially when compared to the school across the bay where every student lives in a home with maids and gardeners and who are handed a school-issued Macintosh laptop in the first week of school.

Please Mr. President Obama, in eradicating NCLB can you please try to change the tone of the debate. Let's stop victimizing the teachers.

Sincerely,
Karen @ Math Me Thinks

Letter to the President Regarding NCLB and Charter Schools

Dear President Obama,

Please read this article by Diane Ravitch from the Washington Post, entitled "Why I Changed My Mind About School Reform". Ms. Ravitch is absolutely correct in her opinion.

My favorite quote from the article,

"They* also fail to recognize that the best predictor of low academic performance is poverty—not bad teachers."

Please read the article Mr. President.

* Refers to the Obama administration, following in the footsteps of NCLB.

Sincerely,
Karen @ Math Me Thinks

What do you say to the kid who asks "What will I ever use this for?"

Well it appears that none other than Euclid had a response for that question. Simon Singh, in Fermat's Enigma, tells a story about Euclid when he was teaching, as the first head of the mathematics department at Alexandria:

"Euclid searched for mathematical truth for its own sake and did not look for applications in his work. One story tells of a student who questioned him about the use of the mathematics he was learning. Upon completing the lesson, Euclid turned to his slave and said, "Give the boy a penny since he desires to profit from all that he learns." The student was then expelled."

If only...

Euclid of Alexandria

Specialization Effect and Its Influence on Memory and Problem Solving in Expert Chess Players

This study says that chess players perform better in a match after they practice specific moves rather than general chess.

From my own experience, success on exams depends on having a deep understanding of the big picture and an ability to memorize a slate of essential algorithms.

I'm wondering if there is a relationship with the chess research?

Teacher Pay Tied to Test Scores - Doesn't Make Sense

The new trend, designed to improve education, is to tie teacher pay to student test scores. All data show that student success is tied to family education, primarily to the education level of the mother, and family resources. So, let's investigate why this is a bad idea through the lens of a story.

Swimming the River

A group of coaches were given a task to teach a group of kids a new stroke. Each group of kids will use the new stroke to swim a given distance on a fast moving river. Each coach will be competing against other coaches for their income level and even the ability to keep their job. Their pay, living, sustenance, will be based on how fast the kids in their group can do this feat. Coaches will face negative repercussions if any kid is left behind and is unable to complete the task.

Who are the kids?

1. Some of the kids have a pool in their backyards. Others, come from families where no one knows how to swim.
2. Some kids' mommies took them to baby swim classes while others' mommies are afraid of the water.
3. Some kids vacation on the lake every summer but others kids have never been out of the city limits.
4. Some of the kids come from families where athletics, exercise, and good nutrition are the norm. But, sadly other kids eat high fat diets and spend their days watching television.
5. There are kids who have private swim coaches, to give them a leading edge in any kind of swim competition, (very important to the parents) and there are even a couple of kids whose families have the means to buy them those fancy hi-tech swim suits.
6. Unfortunately for everyone, there are even a few kids who will sabotage all efforts by trying to dunk other kids or by even refusing to get in the water at all, and others who spend their time doing nothing but splashing the coach. 
7. Some groups of kids will swim against the current while others swim with it.
   
8. The coaches have no power of which kids will be in their group.

The person running this competition, let's call him the 'Principal' will be the person who decides how the kids are grouped and which coach they have. The Principal doesn't know much about swimming… just not his thing. One passionate coach has managed to get herself on his bad side and so, of course, she ends up with the group of kids who are the hardest to coach. This is great for the kids since she is an excellent coach. A sycophantic colleague who spends her time buttering-up the Principal, gets the highest performing group of kids. We will call them the 'honors' kids.

The day of the competition arrives. The group of kids, with the sycophantic coach, wins the competition and as a result that coach gets a $10,000 bonus for that year. The low performing group of kids, with the great coach, does better than expected but of course didn't win. It actually came in last. Their coach loses her job.

The moral of the story:

There are good teachers and bad teachers but you certainly can't tell which they are by the test scores of their students.

DRENCH

http://www.flashbynight.com/drench/

DRENCH by flashbynight - a fun, web-based, strategy game for your math students.

The Science of Motivation

Yet another great T.E.D. talk. Dan Pink talks about business models that have abandoned the 'Carrot and Stick' model for employee motivation.



KQED's Forum also hosted Dan Pink on a discussion about using creativity, right brain, versus narrow thinking to be productive.

I'm wondering how Dan Pink's ideas would work in the classroom???

Get Flurrious

When you make and share a snowflake, Get Flurrious reportedly sends $1 to UNICEF. Making digital snowflakes is a fun activity involving the mathematical concept of symmetry.